Certainly! Let's start by simplifying both sides of the given equation individually and then solve it for [tex]\( x \)[/tex].
The given equation is:
[tex]\[ -2(x + 4) + 3x = -4(3x + 2) + 13 \][/tex]
### Simplify the Left-Hand Side (LHS)
First, expand the terms on the LHS:
[tex]\[ -2(x + 4) + 3x \][/tex]
Distribute [tex]\(-2\)[/tex] through the parenthesis:
[tex]\[ -2x - 8 + 3x \][/tex]
Combine like terms:
[tex]\[ (-2x + 3x) - 8 \][/tex]
[tex]\[ x - 8 \][/tex]
So, the simplified LHS is:
[tex]\[ x - 8 \][/tex]
### Simplify the Right-Hand Side (RHS)
Next, expand the terms on the RHS:
[tex]\[ -4(3x + 2) + 13 \][/tex]
Distribute [tex]\(-4\)[/tex] through the parenthesis:
[tex]\[ -12x - 8 + 13 \][/tex]
Combine the constant terms:
[tex]\[ -12x + 5 \][/tex]
So, the simplified RHS is:
[tex]\[ -12x + 5 \][/tex]
### Setting Both Sides Equal
With the simplified sides of the equation, we have:
[tex]\[ x - 8 = -12x + 5 \][/tex]
### Solving for [tex]\( x \)[/tex]
To solve for [tex]\( x \)[/tex], we first collect all the [tex]\( x \)[/tex]-terms on one side of the equation and the constant terms on the other side:
[tex]\[ x + 12x = 5 + 8 \][/tex]
Combine the [tex]\( x \)[/tex]-terms:
[tex]\[ 13x = 13 \][/tex]
Divide both sides by 13:
[tex]\[ x = 1 \][/tex]
So, the solution to the equation is:
[tex]\[ x = 1 \][/tex]
